MAGMA Computational Algebra System

Supersingular Curves

IsSupersingular(E: parameters) : CrvEll -> BoolElt

    Proof: BoolElt                      Default: true

Given an elliptic curve E over a finite field, this function returns false if E is ordinary, otherwise proves that E is supersingular. If the parameter Proof is set to false, then the effect of the function is the same as that of IsProbablySupersingular.

IsOrdinary(E) : CrvEll -> BoolElt

Given an elliptic curve E over a finite field, this function returns true if the elliptic curve E is ordinary, otherwise false (i.e., if it is supersingular). Thus, this function is the logical negation of IsSupersingular.

IsProbablySupersingular(E) : CrvEll -> BoolElt

Given an elliptic curve E over a finite field, this function returns returns false if the elliptic curve E is proved to be ordinary, otherwise true. The algorithm is nondeterministic, and repeated tests are independent.